AIAA 2006-6753 Revisiting Spacetrack Report #3 David A. Vallado* Center for Space Standards and Innovation, Colorado Springs, Colorado, 80920 Paul Crawford† Crawford Communications Ltd., Dundee, DD2 1EW, UK Richard Hujsak‡ Analytical Graphics, Inc., Exton, PA, 19341 and T. S. Kelso§ Center for Space Standards and Innovation, Colorado Springs, Colorado, 80920 Over a quarter century ago, the United States Department of Defense (DoD) released the equations and source code used to predict satellite positions through SpaceTrack Report Number 3 (STR#3). Because the DoD's two-line element sets (TLEs) were the only source of orbital data, widely available through NASA, this code became commonplace among users needing accurate results. However, end users made code changes to correct the implementation of the equations and to handle rare cases encountered in operations. These changes migrated into numerous new versions and compiled programs outside the DoD. Changes made to the original STR#3 code have not been released in a comprehensive form to the public, so the code available to the public no longer matches the code used by DoD to produce the TLEs. Fortunately, independent efforts, technical papers, and source code enabled us to synthesize a non-proprietary version which we believe is up-to-date and accurate. This paper provides source code, test cases, results, and analysis of a version of SGP4 theory designed to be highly compatible with recent DoD versions. I. INTRODUCTION AND HISTORY he Simplified General Perturbations (SGP) model series began development in the 1960s (Lane 1965), and T became operational in the early 1970s (Lane and Cranford, 1969). The original release of the refined Simplified General Perturbations-4 (SGP4) propagator source code was Spacetrack Report Number 3 (Hoots and Roehrich, 1980). That release resulted from a user compatibility survey of space surveillance operational sites and official users. The magnitude of the resulting variations spurred an effort to promote better compatibility for users. The intent was to get the operational community, as well as ordinary users, synchronized with respect to the implementation. The best vehicle for this was a technical report, including the computer source code. It was designed for the widest possible dissemination. Although most of the equations were given, the use of the source code became common practice for using Two-line Element (TLE) sets.** * Technical Program Manager, Center for Space Standards and Innovation, 7150 Campus Dr, Suite 260, [email protected], AIAA Associate Fellow. † Principal Engineer, 25 Blackness Avenue, [email protected]. ‡ Orbit Determination Lead Engineer, 220 Valley Creek Blvd, [email protected]. § Technical Program Manager, Center for Space Standards and Innovation, 7150 Campus Dr, Suite 260, [email protected], AIAA Associate Fellow. ** Note that the code is not vetted as a consensus standard. The well-confirmed and long-established industry consensus standards process requires consensus on all elements of a technique and its implementation throughout a wide community of experts. There is no formal consensus standard for orbit determination or propagation. 1 American Institute of Aeronautics and Astronautics Spacetrack Report Number 3 officially introduced five orbital propagation models to the user community—SGP, SGP4, SDP4, SGP8 and SDP8—all “generally” compatible with the TLE data. At the time, SGP had just been replaced by SGP4/SDP4 (the latter having included deep-space perturbations). The SGP8/SDP8 model was developed to alleviate deficiencies of SGP4/SDP4 for the special cases of orbital decay and reentry. The approach provided a closed-form solution based on the general trends of orbital elements as they neared reentry, and was quite successful. However, there is no evidence to suggest that SGP8/SDP8 was implemented for operational TLE formation. After STR#3, Spacetrack Report Number 6 (Hoots, 1986) was publicly released by North American Aerospace Defense Command (NORAD). Some researchers initially assumed this release was intended to update portions of the SDP4 deep-space routines, but the actual intention was to document HANDE* and had little to do with SGP4/SDP4. Nevertheless, it provided amateur satellite trackers and researchers with a confirmation of identified deficiencies in the original validation and verification efforts. This report has not been as widely circulated as STR#3, which benefited from its early electronic availability (Kelso, 1988). In the early 1990s, the NASA Goddard Space Flight Center (GSFC) obtained a copy of the 1990 standalone SGP4 code† from project SpaceTrack as part of a study on orbit propagation models for the SeaWiFS Mission (Patt et al., 1993). In 1996–7 they released the unrestricted code on the Internet and to numerous organizations around the world involved in the SeaWiFS Mission. It confirmed changes already discovered by many independent researchers, and we refer to it simply as the “GSFC version.” In 1998, Hoots published a history of the equations, background, and technical information on SGP4. In 2004, Hoots et al. published a complete documentation of all the equations (including the deep-space portion). These publications cover the incorporation of resonances, third-body forces, atmospheric drag, and other perturbations into the mathematical technique. We note that all published reports on SGP4 have suggested only improvements in the code used to implement it, and not any changes to the underlying theory. Thus, the equations in Hoots (2004) should be representative of the current mathematical theory. This is a fundamental and essential assumption we use in this paper. Outside the DoD, perhaps the most comprehensive external version of the software resided with Paul Crawford. His “Dundee code” kept track of the many changes inferred by real-world observations by independent researchers, and those confirmed by DoD releases. Many of the results contained in the code pre-date matters that were later confirmed in the DoD standalone releases. We use the change history from the Dundee in this analysis. A. Motivation Spacetrack Report Number 3 noted the importance of using the specific equations and data input to ensure proper operation and we repeat it here. “The most important point to be noted is that not just any prediction model will suffice… The NORAD element sets must be used with one of the models described in this report in order to retain maximum prediction accuracy.” The numerous releases and modifications to the original SGP4 standalone code have made it virtually impossible to satisfy that direction today. For instance, using element sets generated with the operational SGP4 code will not reproduce the same ephemeris as the original STR#3 code (without modifications) would. Similarly, using this TLE data in another general perturbations propagator will result in completely erroneous results. Simply converting the orbital elements to an osculating state vector and propagating with a numerical propagator is equally invalid. These are consequences of the model-based parameter estimation technique of orbit determination, and are most noticeable when using general perturbation techniques. In fact, one may infer that none of the public releases meet this criterion because Kaya, et al. (2004) says “Air Force Space Command (AFSPC) developed Astrodynamic Standard Software to emulate the operational astrodynamic algorithms used by the Space Control Center (SCC) in the Cheyenne Mountain Operations Center (CMOC)” by “extracting desired algorithms from the larger programs in the Space Defense Operations Center (SPADOC) within the SCC.” Thus, there are multiple versions of the SGP4 code even within the DoD. We must recognize that the true official code is inextricably linked and embedded within the operational computer system at CMOC (we designate it as the “operational” version). CMOC uses this operational version to produce all the TLE data that are distributed daily to worldwide users. A similar “standalone” version of the official code is maintained * The HANDE model was intended to replace the analytical SGP4/SDP4 model. It incorporated the effects of the Jacchia dynamic atmosphere models for the average solar flux during the propagation interval, while retaining the speed and character of an analytic general perturbations model. It also included the full Brouwer gravity solution, much of which had been dropped for the SGP4 simplification. The code was implemented in the operational system, but its use is unknown. † It appears that the merged SGP4/SDP4 models were now referred to simply as ‘SGP4’ from this 1990 code onwards. 2 American Institute of Aeronautics and Astronautics by technical offices within AFSPC, which, under various organizational names,* published the Spacetrack series of reports. The mention of emulating the operational codes leads us to think that AFSPC routinely tests and aligns these two versions for compatibility. Spacetrack Report Number 3 report contained a snapshot of this standalone code in 1980 and is the basis for our discussion. Kaya et al. (2001) note the lack of enforcement for early AFSPC instructions (publicly available administrative documents) concerning the use of their standalone code, and discusses changes in AFSPC policy about releasing code. We see this in the evolution of Air Force Space Command Instructions. These documents imply that models and computer codes have been extracted from larger programs, modified